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# Parallel and perpendicular slopes?

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Given this pair of slopes, what is the value of n if the lines are parallel? What is the value of n if the lines are perpendicular?

$${3 \over n}$$,$$-{7 \over 2}$$

If I cross multiply, the parallel slope is $$n = -{6 \over 7}$$, is that right?

As for perpendicular... how would I solve for that?

Apr 8, 2018

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Parallel lines have the same slope.

If the lines are parallel, then the slopes of the lines are equal.

If the lines area parallel, then....

$$\frac3n\,=\,-\frac72 \\~\\ 3\cdot2\,=\,-7\cdot n \\~\\ 6\,=\,-7n\\~\\ n\,=\,-\frac67$$

....You're right!!!

If the lines are perpendicular, then the slopes are negative reciprocals of each other.

That means   $$\frac3n$$   must equal the negative reciprocal of   $$-\frac72$$  .

The negative reciprocal of   $$-\frac72$$   is    $$\frac27$$  .

If the lines are perpendicular, then....

$$\frac3n\,=\,\frac27\\~\\ 7\cdot3\,=\,2\cdot n\\~\\ 21\,=\,2n\\~\\ n\,=\,\frac{21}{2}$$

.
Apr 8, 2018